Preorder

A Preorder is a concept from Category Theory. ¹

Preorders follow two laws: ¹

• Reflexivity - Each object in the underlying set is either greater than or equal to itself
• Transitivity - if a ≥ b and b ≥ c, then a ≥ c

There is exactly either zero or one morphisms between every pair of objects in a preorder, which makes it a thin category. ² If a preorder is antisymmetric, then it is an order. ¹